# Signals & Systems Questions and Answers – Periodic Signals – 1

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This set of Signals & Systems Multiple Choice Questions & Answers (MCQs) focuses on “Periodic Signals – 1”.

1. What are periodic signals?
a) The signals which change with time
b) The signals which change with frequency
c) The signal that repeats itself in time
d) The signals that repeat itself over a fixed frequency

Explanation: Those signals which repeat themselves in a fixed interval of time are called periodic signals. The continuous-time signal x(t) is periodic if and only if
x(t+T)= x(t).

2. Periodic signals are different in case of continuous time and discrete time signals.
a) True
b) False

Explanation: Periodic signals are same in case of continuous time and discrete time signals.
In case of continuous time signal, x(t)=x(t+T), for all t>0
In case of discrete time signal,
x(n)=x(n+N), for all n>0.

3. What is the time period of a periodic signal in actual terms?
a) The signals which start at t=-∞ and end at t=+∞
b) The signals which have a finite interval of occurrence
c) The signals which start at t= -∞ and ends at a finite time period
d) The signals which have a short period of occurrence

Explanation: The periodic signals have actually a time period between t=-∞ and at t= + ∞. These signals have an infinite time period, that is periodic signals are actually continued forever. But this is not possible in case of real time signals.
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4. Periodic signals actually exist according to a definition.
a) True
b) False

Explanation: Periodic signals are defined as signals having time period in between t=-∞ and t=+ ∞. These signals have an infinite time period that is periodic signals are continued forever. But real time signals always cease at some time due to distortion and resistance.

5. What is a fundamental period?
a) Every interval of a periodic signal
b) Every interval of an aperiodic signal
c) The first interval of a periodic signal
d) The last interval of a periodic signal

Explanation: The first time interval of a periodic signal after which it repeats itself is called a fundamental period. It should be noted that the fundamental period is the first positive value of frequency for which the signal repeats itself.

6. Comment on the periodicity of a constant signal?
a) It is periodic
b) It is not periodic
c) It is a mixture of period and aperiodic signal
d) It depends on the signal

Explanation: A constant signal is not periodic. It is because it does not repeat itself over in time. It is constant at any time, it is aperiodic.

7. A discrete time periodic signal is defined as x(n)= x(n+N)
How is the N defined here?
a) Samples/ cycle
b) Samples/ twice cycle
c) Fundamental period
d) Rate of change of the period

Explanation: The value of N is a positive integer and it represents the period of any discrete time periodic signal measured in terms of number of sample spacing ( samples/cycle). The smallest value of N is a fundamental period.

8. What is the general range of a period of a signal?
a) It can have of any value from positive to negative
b) It can be negative
c) It can be positive
d) It is always positive

Explanation: The period of a periodic signal is always positive. The smallest positive value of a periodic interval is called a fundamental period in case of both discrete and continuous time signal.

9. What is the area of a periodic signal in a periodic interval?
a) It depends on the situation
b) It is same as the area in the previous interval
c) It is different in different situations
d) It is the square of the fundamental period

Explanation: The area of any periodic signal in any interval is the same. Hence it is same as the previous interval. This results from the fact that a periodic signal takes same values at the intervals of T.

10. When is the sum of M periodic signals periodic?
a) T/Ti = 1
b) T/Ti = 4
c) T/Ti = ni
d) T/Ti = m+n

Explanation: The sum of M periodic signal is not necessarily periodic. It is periodic only with the condition that
T/Ti = ni, 1≤i≤M,
where Ti is the period of the signal and in the sum of ni is an integer.

11. How is the period of the sum signal computed as?
a) T*n
b) T*T
c) T*N+M
d) T *(n+m)

Explanation: If a signal is periodic then we have to convert each of the periods to the ratio of integers. We have to take the ratio of greatest common divisor(gcd) from the numerator to the gcd of denominator. The LCM of the denominators of the resulting ratios is the value of n the period of the sum signal is T*n.

12. What is the necessary and sufficient condition for a sum of a periodic continuous time signal to be periodic?
a) Ratio of period of the first signal to period of other signals should be constant
b) Ratio of period of the first signal to period of other signals should be finite
c) Ratio of period of the first signal to period of other signals should be real
d) Ratio of period of first signal to period of other signal should be rational

Explanation: The necessary and sufficient condition for a sum of a periodic continuous time signal to be periodic is that the ratio of a period of the first signal to the period of other signals should be rational.
I.e T/Ti = a rational number.

13. Under what conditions the three signals x(t), y(t) and z(t) with period t1 t2 and t3 respectively are periodic?
a) t1/t2= t2/t3
b) t1/t2 is rational
c) All the ratios of the three periods in any order is rational
d) t1/t2/t3= rational

Explanation: if x(t) , y(t) and z(t) are to be periodic then,
t1/t2 should be rational and simultaneously
t1/t3 should be rational and
t2/t3 should be rational. Hence, all the ratios of the three periods in any order is rational.

14. What is the fundamental period of the signal : ejwt?
a) 2π/w
b) 2π/w2
c) 2π/w3
d) 4π/w

Explanation: The complex exponential signal can be represented as
ejwt= ejwt+jwT
Hence, wt=2 π,
T= 2π/w.

15. What is the period of the signal :jejw11t?
a) 2π/10
b) 2π/11
c) 4π/10
d) 4π/11

Explanation: From the definition of periodic signal, we express a periodic exponential signal as :
ejw11t= ejwt+jwT
Hence, 11wt=2 π,
which gives the fundamental period as
2π/11.

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